The Hausmann-Weinberger invariant of a group G is the minimal Euler characteristic of a closed orientable 4-manifold M with fundamental group G. We compute this invariant for finitely generated free abelian groups and estimate the invariant for all finitely generated abelian groups.
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5 results for “Hausmann-Weinberger”
Two types of 4-manifolds disagree on minimum Euler characteristic.
problem Disagreement between topological and smooth 4-manifolds.
method Comparison of topological and smooth 4-manifolds with a fixed fundamental group.
result Minimum Euler characteristic differs between topological and smooth 4-manifolds.
Study invariants of 3-manifold groups to determine Euler characteristics of 4-manifolds.
problem Determine Euler characteristics of 4-manifolds with 3-manifold groups.
method Use invariants from Hausmann-Weinberger, Kotschick, and Hillman to address specific cases.
result Identify conditions under which specific Euler characteristics are equal.
In this note we prove that Thompson's group F cannot be the fundamental group of a symplectic 4-manifold with trivial canonical class by showing that its Hausmann-Weinberger invariant q(F) is strictly positive.
New bounds on Euler characteristics for certain manifolds with finite groups.
problem Estimating Euler characteristics of specific topological manifolds.
method Defining a new invariant and using cohomological invariants of fundamental groups.
result Established new bounds on minimal Euler characteristics for 4-manifolds.